Câu hỏi của tuan anh le

Question

chưng minh 3^2005 +3^2006 +3^2007+3^2008+ 3^2009 chi hết cho 11

Hoang Hung Quan · Accepted Answer

Ta có:

$3^{2005}+3^{2006}+3^{2007}+3^{2008}+3^{2009}$

$=3^0.3^{2005}+3^1.3^{2005}+3^2.3^{2005}+3^3.3^{2005}$ $+3^4.3^{2005}$

$=3^{2005}\left(3^0+3^1+3^2+3^3+3^4\right)$

$=3^{2005}.121=3^{2005}.11.12⋮11$

Vậy $3^{2005}+3^{2006}+3^{2007}+3^{2008}+3^{2009}⋮11$ (Đpcm)

Câu trả lời:

Ta có:

$3^{2005}+3^{2006}+3^{2007}+3^{2008}+3^{2009}$

$=3^0.3^{2005}+3^1.3^{2005}+3^2.3^{2005}+3^3.3^{2005}$ $+3^4.3^{2005}$

$=3^{2005}\left(3^0+3^1+3^2+3^3+3^4\right)$

$=3^{2005}.121=3^{2005}.11.12⋮11$

Vậy $3^{2005}+3^{2006}+3^{2007}+3^{2008}+3^{2009}⋮11$ (Đpcm)